This work looks at the stiffness matrix of some simple but very general systems of springs supporting a rigid body. The stiffness matrix is found by symbolically differentiating the potential function. After a short example attention turns to the general structure of the stiffness matrix and in particular the principal screws introduced by Ball.

In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises’ invaria...

[A] matrix with constants describing the anisotropy of the material [B] strain matrix [BL] linear strain matrix [BNL] nonlinear strain matrix c speed of sound d rate of deformation tensor dp plastic rate of deformation D elastic constitutive tensor [D] matrix of the elastic constitutive tensor [DT] matrix form of the constitutive tensor ds lengths of the vector dx dS lengths of the vector dX dv...

A model-based diagnostic methodology is proposed for the dimensional fault diagnosis of compliant beam structures in automotive or aerospace assembly processes. In the diagnosis procedure, the product measurement data are used to detect and isolate dimensional faults caused by part fabrication error in compliant beam assemblies. The proposed method includes a predetermined fault patterns model ...

The myofibroblastic differentiation of hepatic stellate cells (HSC) is a critical event in liver fibrosis and is part of the final common pathway to cirrhosis in chronic liver disease from all causes. The molecular mechanisms driving HSC differentiation are not fully understood. Because macroscopic tissue stiffening is a feature of fibrotic disease, we hypothesized that mechanical properties of...

for the nonlinear analysis of structures using the well known newton-raphson method, the tangent stiffness matrices of the elements must be constructed in each iteration. due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the newton-raphson method to reduce the cost and time required by the analysis. in this paper, a ...

In this article an analysis is presented to the problem of characterizing the accuracy of deterministic localization of fixtures. In a statistical framework, the positioning accuracy of the workpiece localized by the locators of a fixture is described by a symmetric, positive-definite accurateness matrix (or variance matrix). The accurateness (variance) matrix is identified to have similar stru...

This talk is concerned with the P1 finite element approximation of the eigenvalue problem of second-order elliptic operators subject to the Dirichlet boundary condition. The focus is on the preservation of basic properties of the principal eigenvalue and eigenfunctions of continuous problems. We shall show that when the stiffness matrix is an irreducible M-matrix, the algebraic eigenvalue probl...

Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped atherma...

For the nonlinear analysis of structures using the well known Newton-Raphson Method, the tangent stiffness matrices of the elements must be constructed in each iteration. Due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the Newton-Raphson method to reduce the cost and time required by the analysis. In this paper, a ...